Question:
If
\[
\frac{4}{x+y}+\frac{2}{x-y}=2
\]
and
\[
\frac{3}{x+y}+\frac{1}{x-y}=\frac54
\]
then \(y:x=\)
If
\[
\frac{4}{x+y}+\frac{2}{x-y}=2
\]
and
\[
\frac{3}{x+y}+\frac{1}{x-y}=\frac54
\]
then \(y:x=\)
Show Hint
Substitute reciprocal terms to convert fractions into linear equations.
Updated On: Jul 15, 2026
- \(3:1\)
- \(1:3\)
- \(2:1\)
- \(1:2\)
Show Solution
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The Correct Option is B
Solution and Explanation
Let:
\[
a=\frac1{x+y},\quad b=\frac1{x-y}
\]
Then:
\[
4a+2b=2 \Rightarrow 2a+b=1
\]
\[
3a+b=\frac54
\]
Subtracting:
\[
a=\frac14
\]
Substitute:
\[
2\left(\frac14\right)+b=1
\]
\[
b=\frac12
\]
So:
\[
x+y=4,\quad x-y=2
\]
Adding:
\[
2x=6 \Rightarrow x=3
\]
\[
y=1
\]
Hence:
\[
y:x=1:3
\]
\[
\boxed{1:3}
\]
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